https://elib.bsu.by:443/handle/123456789/162704 NPCS Vol.18, no.3, pp. 284-409 (2015) 2026-04-20T10:13:27Z https://elib.bsu.by:443/handle/123456789/163181 Заглавие документа: Microwave Experiments in Complex Systems: From Quantum Chaos to Monster Waves Авторы: Stockmann, H.-J. Аннотация: Microwave experiments have become an important tool to study wave transport in chaotic and disordered systems. This includes both matter waves in quantum-mechanical systems as well as various types of classical waves. This short report introduces into the technique and gives a number of illustrative examples. It addresses mainly non-expert readers to give them the chance to become acquainted with the method without the need to study additional literature. 2015-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/163180 Заглавие документа: Chronotaxic Systems: A Simple Paradigm to Treat Time-Dependent Oscillatory Dynamics Stable under Continuous Perturbation Авторы: Barabash, M. L.; Suprunenko, Y. F.; Stefanovska, A. Аннотация: The treatment of non-autonomous systems is a challenging task, and one that arises in many branches of physics and science in general. The recently introduced notion of chronotaxic systems provides a new and promising approach to the problem. Chronotaxic dynamics is characterized by a time-dependent point attractor which exists in the time-dependent contraction region. Chronotaxic systems are therefore capable of resisting continuous external perturbations while being characterised by complex time-dependent dynamics. The theory of chronotaxic systems, reviewed in this paper, together with corresponding inverse approach methods developed to tackle such systems, makes it possible to identify the underlying deterministic dynamics and to extract it. The resultant reduction of complexity may be useful in various scientific applications, especially in living systems. 2015-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/163176 Заглавие документа: Some Analytical Aspects of the Nonlinear Fourier Transform Авторы: Saksida, P. Аннотация: The inverse scattering transform method for solving nonlinear integrable partial di˙erential equations is a nonlinear analogue of the Fourier transform method for solving suitable initial-value problems for linear partial di˙erential equations. Therefore, the scattering transform is often called the nonlinear Fourier transform. The nonlinear Fourier transform F and its inverse G are analytically computable only for some very special arguments. Therefore, it makes sense to look for perturbational approximations of these transforms. In the paper, we propose an iterative method for constructing arbitrarily good approximations of G for an arbitrary argument. We discuss analytical properties which guarantee that the iterative formula for G converges. We also provide an explicit convergent power series for the calculation of F in powers of the spectral parameter. We expect that this formula will be useful in the study of certain analytical properties of F described by the Paley-Wiener type of theorems. 2015-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/163155 Заглавие документа: Statistical Properties of One-dimensional Time-dependent Hamilton Oscillators: From the Parametrically Adiabatic Driving to the Kicked Systems Авторы: Robnik, M. Аннотация: Time-dependence of a Hamilton system models its interaction with the environment and such systems are recently of great interest in many di˙erent contexts. We review the recent studies of the parametrically driven one-dimensional Hamilton oscillators, their time evolution and the statistical properties of the energy, starting from a microcanonical ensemble. In the case of adiabatic driving the energy remains sharply distributed (Dirac delta function), and its value follows the adiabatic law. If the driving is not adiabatic, the energy becomes distributed, as its value depends on the initial condition. For the linear oscillator this distribution is rigorously derived to be the arcsine distribution for any parametric driving law and the value of the adiabatic invariant (or action) at the mean energy always increases. The mean energy and the variance can be calculated for a few exactly solvable cases, and in the general case we apply the rigorous WKB method developed by Robnik and Romanovski (2000). In the nonlinear oscillators this universality is lost. The adiabatic invariant (action) at the mean energy can decrease for nonadiabatic but slow changes, while in another extreme case of fast parametric variation, in particular for a kick (jump), almost always increases, and so does the Gibbs entropy. This is shown for a number of exactly solvable cases, and a local analysis is o˙ered for the general oscillators. In the case of a monotonic driving of homogeneous power law potentials the nonlinear WKB method developed by Papamikos and Robnik (2012) is applied and shown to be highly accurate. The periodic kicking is also investigated. The relation to the statistical mechanics in the sense of Gibbs is explained. 2015-01-01T00:00:00Z